Advanced Search
Article Contents
Article Contents
Early Access

Early Access articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Early Access publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Early Access articles via the “Early Access” tab for the selected journal.

Degree of convergence of a function in generalized Zygmund space

  • *Corresponding author: M. Mursaleen

    *Corresponding author: M. Mursaleen 
Abstract Full Text(HTML) Figure(2) / Table(2) Related Papers Cited by
  • In this paper, we obtain the results on the degree of convergence of a function of Fourier series in generalized Zygmund space using deferred Cesàro-generalized Nörlund $ (D^{h}_{g}N^{a,b}) $ transformation. Important corollaries are deduced from our main results. Some applications are also given in support of our main results.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


    \begin{equation} \\ \end{equation}
  • 加载中
  • Figure 1.  Degree of convergence of function $ f $

    Figure 2.  Degree of convergence of function $ f $

    Table 1.  Degree of convergence of $f$ for different $n$

    $n$ Degree of convergence of $f$
    100 1.2575829
    1000 1.1507909
    10000 1.1082121
    50000 1.0911295
    100000 1.0854078
    500000 1.0746045
    1000000 1.0707630
    . .
    . .
    $\infty$ 1
     | Show Table
    DownLoad: CSV

    Table 2.  Degree of convergence of $f$ for different $n$

    $n$ Degree of convergence of $f$
    100 3.8368
    1000 3.5991
    10000 3.4794
    50000 3.4274
    100000 3.4096
    500000 3.3759
    1000000 3.3639
    10000000 3.3315
    100000000 3.3073
    . .
    . .
    $\infty$ 3.1416
     | Show Table
    DownLoad: CSV
  • [1] R. P. Agnew, On deferred Cesàro means, Ann. Math., 33 (1932), 413-421.  doi: 10.2307/1968524.
    [2] C. K. Chui, An Introduction to Wavelets, Wavelet Analysis and its Applications, 1. Academic Press, Inc., Boston, MA, 1992.
    [3] G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949.
    [4] S. Lal, Approximation of functions belonging to the generalized Lipschitz class by $C_{1}N_{p}$ summability method of Fourier series, Appl. Math. Comput., 209 (2009), 346-350.  doi: 10.1016/j.amc.2008.12.051.
    [5] S. Lal and A. Mishra, The method of summation $(E, 1)(N, p_{n})$ and trigonometric approximation of function in generalized Hölder metric, J. Indian Math. Soc., 80 (2013), 87-98. 
    [6] B. A. London, Degree of Approximation of Hölder Continuous Functions, Thesis (Ph.D.)-University of Central Florida, 2008.
    [7] Det Kgl. Mollerup, Danske videnskabernes selska, Math.-Fys. Medd., 3 (1920).
    [8] H. K. Nigam, Degree of approximation of a function belonging to weighted $(L_{r}, \xi(t))$ class by $(C, 1)(E, q)$ means, Tamkang J. Math., 42 (2011), 31-37.  doi: 10.5556/j.tkjm.42.2011.514.
    [9] H. K. Nigam and Md. Hadish, Approximation of a function in Hölder class using double Karamata $(K^ {\lambda, \mu})$ method, Eur. J. Pure Appl. Math., 13 (2020), 567-578.  doi: 10.29020/nybg.ejpam.v13i3.3663.
    [10] H. K. Nigam and Md. Hadish, Best approximation of functions in generalized Hölder class, J. Inequal. Appl., (2018), Paper No. 276, 15 pp. doi: 10.1186/s13660-018-1864-y.
    [11] H. K. Nigam and Md. Hadish, Trigonometric approximation of functions by Hausdorff-Matrix product operators, Nonlinear Functional Analysis and Applications, 24 (2019), 675-689. 
    [12] H. K. Nigam and S. Rani, Approximation of function in generalized Hölder class, Eur. J. Pure Appl. Math., 13 (2020), 351-368.  doi: 10.29020/nybg.ejpam.v13i2.3667.
    [13] E. C. TitchmarshThe Theory of Functions, Second edition, Oxford University Press, Oxford, 1939. 
    [14] O. Töeplitz, Uberallagemeine lineara, Mittelbil. Dunger. P.M.F., 22 (2013), 113-119. 
    [15] A. ZygmundTrigonometric Series, 3rd rev. ed., Cambridge University Press, Cambridge, 2002. 
  • 加载中




Article Metrics

HTML views(174) PDF downloads(243) Cited by(0)

Access History



    DownLoad:  Full-Size Img  PowerPoint